m₂ + m₂ 2 - m₂ 2 3 2 m₂ 2 m₂ с {x} + [ C c]{*}+[(* m₂ = 1kg m₂ = 2kg k₁ = K₂ =k₂ = 1%/m W1₂ Determine (analytically do not use MatLab): 1) The characteristic equation 2) The natural frequencies 3) The mode shapes normalized to the largest value =1.0 4) Sketch the mode shapes 6) Determine the solutions 5) Show the mode shapes are orthogonal with respect to the mass matrix x₂ (1) and x₂ (1) for }-{-¹} mm X10 using the modal method. 7) Plot your results using MatLab. X₂0 11 Wn₂ Wn₂ = .1.7552 rad/s −4k₂ [(k₂ + 4k₂+k₂) -4k₂ M(t) R 30-2 M(t) =.7207 rad/s 0.7016) 11 = 1.0 x₁ (t) = 7.1664 sin(.72071-.00719)+8.7643 sin 1.1552t +2.9678) x₂ (1)= 10.2149 sin(.72071-.00719) — 1.5372 sin 1.1552t +2.9678) = = {-0.1754} [*}-{2}- mm/sec R
m₂ + m₂ 2 - m₂ 2 3 2 m₂ 2 m₂ с {x} + [ C c]{*}+[(* m₂ = 1kg m₂ = 2kg k₁ = K₂ =k₂ = 1%/m W1₂ Determine (analytically do not use MatLab): 1) The characteristic equation 2) The natural frequencies 3) The mode shapes normalized to the largest value =1.0 4) Sketch the mode shapes 6) Determine the solutions 5) Show the mode shapes are orthogonal with respect to the mass matrix x₂ (1) and x₂ (1) for }-{-¹} mm X10 using the modal method. 7) Plot your results using MatLab. X₂0 11 Wn₂ Wn₂ = .1.7552 rad/s −4k₂ [(k₂ + 4k₂+k₂) -4k₂ M(t) R 30-2 M(t) =.7207 rad/s 0.7016) 11 = 1.0 x₁ (t) = 7.1664 sin(.72071-.00719)+8.7643 sin 1.1552t +2.9678) x₂ (1)= 10.2149 sin(.72071-.00719) — 1.5372 sin 1.1552t +2.9678) = = {-0.1754} [*}-{2}- mm/sec R
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
Please solve using matlab
![(3000*30*
[(k₂ + 4k₂ +k₂) -4k₂ x₂
{*} + [ ² ] {*} [^^ +
m₂
m₁+·
m₂
2
2
2
m₂
m₂
m₁ = 1kg m₂ = 2kg k₁=k₂ = k₁ = 1%/m
11
Determine (analytically do not use MatLab):
1) The characteristic equation
2) The natural frequencies
3) The mode shapes normalized to the largest value =1.0
4) Sketch the mode shapes
6) Determine the solutions
5) Show the mode shapes are orthogonal with respect to the mass matrix
x₂ (1) and x₂ (1) for
10
X20
using the modal method.
7) Plot your results using MatLab.
W = .7207 rad/s Wn₂ =.1.7552 rad/s
= {0.700)
11 =
-4k₂
1.0
-0.1754)
mm
4k₂
10
10]
10
mm/sec
x₁ (t) = 7.1664 sin(.7207t—.00719)+8.7643 sin 1.1552t +2.9678)
x₂ (t)=10.2149 sin(.7207t-.00719)-1.5372 sin 1.1552t+2.9678)
M(t)
R
M(t)
R](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b8502c6-77e6-4ad1-93a4-15893327988c%2F8126a4d9-e738-4972-b14e-4dcf1bd1187e%2Fyoaap2e_processed.png&w=3840&q=75)
Transcribed Image Text:(3000*30*
[(k₂ + 4k₂ +k₂) -4k₂ x₂
{*} + [ ² ] {*} [^^ +
m₂
m₁+·
m₂
2
2
2
m₂
m₂
m₁ = 1kg m₂ = 2kg k₁=k₂ = k₁ = 1%/m
11
Determine (analytically do not use MatLab):
1) The characteristic equation
2) The natural frequencies
3) The mode shapes normalized to the largest value =1.0
4) Sketch the mode shapes
6) Determine the solutions
5) Show the mode shapes are orthogonal with respect to the mass matrix
x₂ (1) and x₂ (1) for
10
X20
using the modal method.
7) Plot your results using MatLab.
W = .7207 rad/s Wn₂ =.1.7552 rad/s
= {0.700)
11 =
-4k₂
1.0
-0.1754)
mm
4k₂
10
10]
10
mm/sec
x₁ (t) = 7.1664 sin(.7207t—.00719)+8.7643 sin 1.1552t +2.9678)
x₂ (t)=10.2149 sin(.7207t-.00719)-1.5372 sin 1.1552t+2.9678)
M(t)
R
M(t)
R
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